An arrow is horizontally projected from the top of a tower with an initial velocity of 15m/s.if it reaches the ground 7seconds later,calculate the height of the tower (let g=10m/s0).
S=1/2*g*t*t, h=1/2*10*7*7 h=5*49=245m
H=1/2gt²
H=1/2×10×7²
H=1/2×10×49
H=1/2×490
H=245m
h = 0.5g*t^2.
Well, let's see if I can calculate the height of the tower without falling flat on my face! 😉
We can use the equation of motion to solve this problem. The horizontal velocity remains constant throughout the motion, so we can say that the horizontal component of the arrow's initial velocity is 15 m/s.
Since it takes 7 seconds for the arrow to reach the ground, we can use the equation for vertical displacement to find the height of the tower:
Vertical displacement = Initial vertical velocity * time + (1/2) * acceleration * time^2
Now, the initial vertical velocity of the arrow is 0 m/s because it's horizontally projected. The acceleration due to gravity is 10 m/s^2 (downwards).
Plugging in the values, we get:
Vertical displacement = 0 * 7 + (1/2) * 10 * (7^2)
Simplifying the equation:
Vertical displacement = 245 meters
So, the height of the tower is 245 meters. Just make sure you don't shoot any other arrows at it... it might not be as forgiving as me! 🤡
To calculate the height of the tower, we can use the equation of motion for vertical projectile motion:
h = u*t + (1/2)*g*t^2
where:
h = height of the tower
u = initial vertical velocity (0 m/s since the arrow is horizontally projected)
t = time taken for the arrow to reach the ground (7 seconds)
g = acceleration due to gravity (10 m/s^2)
Since the arrow is horizontally projected, its initial vertical velocity is zero. Therefore, the equation simplifies to:
h = (1/2)*g*t^2
Substituting the given values:
h = (1/2)*10*(7^2)
h = 0.5*10*49
h = 245 meters
Therefore, the height of the tower is 245 meters.
x[f]=at^2/2+v[i]t+x[i]
Brackets dennote a subscript.
You're given x[f], a, t,and v[i]. You can just plug in their values into the formula and solve for x[i]. The horizontal velocity is irrelevant, the height of the tower is the initial position of the arrow, and final position is gonna be when it reaches the ground,or 0.